Pi-Power Odd Exponentiated G-family of Distributions: Statistical Inferences and Application

Abstract

This study presents a new probability distributions family developed using the Pi-power transformation approach. Among this broader class, the study concentrates on one particular distribution whose hazard rate can take on several important shapes, with bathtub, J-shaped, reverse-J, and strictly increasing forms. The main mathematical characteristics of this distribution are discussed and derived, and we estimated its parameters using the method of maximum likelihood.\\ To assess how well the estimation procedure performs, a simulation study is carried out. The results show that both the bias and mean squared error decrease steadily as the sample size grows, and the method performs reasonably well even with relatively small samples. The usefulness of the presented model is further demonstrated through applications to three real datasets drawn from weather and engineering contexts. Two of them are right-skewed, and one data set is symmetrical. Model adequacy measures and goodness-of-fit tests indicate that this distribution offers a better fit than some models taken under study. Overall, the proposed distribution offers a flexible tool for studying hazard behavior and survival-type data, through potential applications across multiple scientific and engineering fields, while also contributing to the broader literature on probability theory, statistical modeling, and inferences.